1. Spring 2007EE130 Lecture 10, Slide 1 Lecture #10 OUTLINE Poisson’s Equation Work function Metal-Semiconductor Contacts – equilibrium energy-band diagram – depletion-layer width Read: Chapter 5.1.2,14.1, 14.2

2. Spring 2007EE130 Lecture 10, Slide 2 Gauss’s Law:  s : permittivity (F/cm)  : charge density (C/cm 3 ) Poisson’s Equation E(x)E(x) E (x+  x) xx area A

3. Spring 2007EE130 Lecture 10, Slide 3 Charge Density in a Semiconductor Assuming the dopants are completely ionized:  = q (p – n + N D – N A )

4. Spring 2007EE130 Lecture 10, Slide 4 Work Function  M : metal work function  S : semiconductor work function  0 : vacuum energy level

5. Spring 2007EE130 Lecture 10, Slide 5 There are 2 kinds of metal-semiconductor contacts: rectifying “Schottky diode” non-rectifying “ohmic contact” Metal-Semiconductor Contacts

6. Spring 2007EE130 Lecture 10, Slide 6

7. Spring 2007EE130 Lecture 10, Slide 7 Ideal MS Contact:  M >  S, n-type Band diagram instantly after contact formation: Equilibrium band diagram: Schottky Barrier :

8. Spring 2007EE130 Lecture 10, Slide 8 Ideal MS Contact:  M <  S, n-type Band diagram instantly after contact formation: Equilibrium band diagram:

9. Spring 2007EE130 Lecture 10, Slide 9

10. Spring 2007EE130 Lecture 10, Slide 10 Ideal MS Contact:  M <  S, p-type  MM  Si  Bp W qV bi =  Bp – (E F – E v ) FB p-type Simetal EvEv EFEF EcEc EoEo  Bp =  + E G -  M

11. Spring 2007EE130 Lecture 10, Slide 11 Effect of Interface States on  Bn EoEo  MM  Si  Bn W qV bi =  B – (E c – E F ) FB n-type Simetal EvEv EFEF EcEc  M >  S Ideal MS contact:  Bn =  M –  Real MS contacts:  A high density of allowed energy states in the band gap at the MS interface pins E F to the range 0.4 eV to 0.9 eV below E c

12. Spring 2007EE130 Lecture 10, Slide 12  Bn tends to increase with increasing metal work function Schottky Barrier Heights: Metal on Si

13. Spring 2007EE130 Lecture 10, Slide 13 Silicide-Si interfaces are more stable than metal-silicon interfaces. After metal is deposited on Si, a thermal annealing step is applied to form a silicide-Si contact. The term metal-silicon contact includes silicide-Si contacts. Schottky Barrier Heights: Silicide on Si

14. Spring 2007EE130 Lecture 10, Slide 14 The Depletion Approximation The semiconductor is depleted of mobile carriers to a depth W  In the depleted region (0  x  W ):  = q (N D – N A ) Beyond the depleted region (x > W ):  = 0

15. Spring 2007EE130 Lecture 10, Slide 15 Electrostatics Poisson’s equation: The solution is: E E E

16. Spring 2007EE130 Lecture 10, Slide 16 Depleted Layer Width, W At x = 0, V = -V bi W decreases with increasing N D

17. Spring 2007EE130 Lecture 10, Slide 17 Summary: Schottky Diode (n-type Si) Equilibrium (V A = 0) -> E F continuous, constant   Bn =  M –  EoEo  MM  Si  Bn W qV bi =  Bn – (E c – E F ) FB n-type Simetal EvEv EFEF EcEc  M >  S Depletion width:

18. Spring 2007EE130 Lecture 10, Slide 18 Summary: Schottky Diode (p-type Si)  MM  Si  Bp W qV bi =  Bp – (E F – E v ) FB p-type Simetal EvEv EFEF EcEc EoEo  M <  S Equilibrium (V A = 0) -> E F continuous, constant  Bp =  + E G -  M Depletion width: